Friday, October 06, 2006

Recap from Lyon (II)

Philip Maini is one of the most entertaining speakers (entertaining in the good sense, of course) in the European biomathematical community. Prof. Maini is the director of the Centre of Mathematical Biology at Oxford University and gave in Lyon a talk entitled "Modeling aspects of cancerous tumour dynamics".

The modeling aspects he mentions are three different projects:

1) The first project, in which he collaborates with people like Gatenby (Arizona) and Gavaghan (Oxford) studies the acid mediated invasion hypothesis.
According to (my interpretation of) this hypothesis, when tumour cells lack oxygen and start to starve then a mutation might appear that would make some cancer cells switch to what is called glycolitic phenotype. This means that these cells have an alternative metabolism that works without oxygen and that is not as efficient as the regular one. The reason why this alternative phenotype has a chance of success is because the waste produced (galatic acid) can be used to degrade the extra cellular matrix and lead to invasion of other tissue. Gatenby, Gavaghan and Maini came with a model in which tumours contain cells with the glycolitic phenotype. The results is that tumours are not benign and that an possible explanation for the existence of necrotic cores (material generated when cells die disorderly because of starvation) can be the result of too much acidification of the environment, even for acid-resistant glycolitic-type tumour cells.

2) Metabolic changes during carcinogenesis. Also with Gavaghan and Gatenby and referring to research covered by a paper in Nature reviews cancer (vol 4, 891-889, 2004). They study somatic evolution in a system in which tumour cells can be of one of three different types: hyperplastic, glycolitic or acid-resistant. These cells inhabit the space of a 2D lattice in which there is oxygen, glucose and hydrogen that diffuse in a continuous manner. Altering the reach and concentration of these elements leads to different numbers of cells displaying one or the other phenotype.

For me this is a good place in which to see how game theory could be used to study the interactions of different players (cancer cells) using different strategies (the different phenotypes) to maximise their payoff from the environment (O,H,glucose).

3) Together with Benjamin Ribba (Lyon, organiser of the workshop and one guy I am working with as of lately) Maini works on a multiscale model on which to study the differences between the vasculature generated by the normal process of vasculogenesis and the ones generated by tumour cells capable of angiogenesis. One of the conclusions he mentioned: don't trust parameters.

Thursday, October 05, 2006

Mansury, Diggory and Deisboeck: Evolutionary game theory in an agent based brain tumor model: exploring the 'genotype-phernotype' link

Mansury et al. JTB 238 (2006) 146-156.

One of the things I had in mind when I started this blog is that I could use it to force me to write reviews about some of the most relevant papers that I often read for my own 'dirty' purposes. Usual reasons apply: it is good to write about what you read since synthesis helps understanding.

In any case, as you know, one of the topics I am interested on is cancer research using evolutionary game theory and although evolution is not what these people have studied the other important keywords are present in this paper.

Mansury et al have devised a nice spatial (2D lattice) agent based (Cellular Automata style) system in which tumour cells inhabit a space with nutrients. Tumour cells can be found in two varieties: A (proliferative) and B (migratory). Non evolutionary game theory is used to analyse the interactions between cells that have different phenotypes and how those interactions reflect on the payoffs of the individual cells and on the tumour as a whole. The payoffs in this game are slightly more complicated (and according to the authors, more realistic) than those of other games. The payoff of a cells is made of three different factors: communication payoff, proliferation payoff and migration payoff.

For the simulations (since it is quite difficult to come with a nice analytical study) they run CAs with 500x500 lattices in which nutrients are diffused from the centre and the middle. From here they study how changing the payoff table results in different velocity of tumour growth, different tumour surface roughness (useful to analyse the malignancy of a tumour) and the numbers of both tumour populations with time

From my point of view, the most significant shortcoming of an otherwise interesting piece of research (and acknowledged by the authors) is the lack of evolution in the model. With evolution out of the equation the condition under which phenotypes emerge and take over the original population cannot be studied. One of the nice features of game theory is that it can be used to study the equilibrium states of tumour cell populations when those tumours are studied as composed of individual cells (or agents in Mansury's et al model). Since the author's know this I am looking forward their next paper to see how the improved model can be used to study carcinogenesis.

Tuesday, October 03, 2006

Richard Dawkins interview

Nice interview in BBC of Richard Dawkins. Here he talks about his latest book The god delusion. Will be buying it as soon as it comes to Dresden (which is unlikely to be any time soon :().

Find the interview here

Recap from Lyon (I)

As I mentioned in a previous post one of the nice talks in Lyon came from Vito Quaranta, from Vanderbilt University in Nashville, USA.

He is and MD collaborating with researchers in the States and Europe (eg Sandy Anderson from Dundee) to develop models on tumour invasion. That is the defining feature that separates tumours from benign to malign (eg cancer).

In order to know if a cancer is invasive MDs tend to look at the way the tumour grows. A tumour with a smooth margin is unlikely to be invasive whereas one with fingering is likely to be so.

Of course I am interested to know if there are alternative studies that could be used to predict the evolution of the cancer that are not based on how the tumour shape looks like. First because in many cases physicians don't have accurate images of the contour of tumours (or sometimes haven't got enough information about what is the result of tumour growth). Second, and maybe most important, because the current shape of a tumour doesn't say much about the potential evolution of it towards malignancy. Maybe a different measure (based on the phenotypic composition of tumour cells) could help not only to tell if a tumour is malignant or benign but if the chances of becoming invasive are high or not.

In any case his presentation showed some interesting results on how the microenvironment affects the evolution of the cancer. Homogeneous microenvironments, that is, those in which space can be created with the same ease everywhere, lead to smooth contours whereas inhomogeneous ones lead to fingering. Interestingly these inhomogeneous microenvironments tend to lead to tumours with little diversity in terms of phenotype: when it is difficult for a tumour cell to create space only invasive phenotypes tend to survive.